Nevanlinna integrated counting function
= Nevanlinna integrated counting function
{c}
{title2=$N(r,f)=n(0,f)\log r+\int_0^r\frac{n(t,f)-n(0,f)}t\,dt$}
The number $n(t,f)$ counts <poles> in $|z|<t$ with <multiplicity>, and $n(0,f)$ is the pole order at zero. Thus $N(r,f)=n(0,f)\log r+\sum_{0<|p|<r}\log(r/|p|)$. Applying this to $1/(f-a)$ counts occurrences of the value $a$.